If your demand for renting videos is Q = 5 − 2P,should you purchase the annual membership from a video store that charges $0.5 per rental,plus an annual membership fee of $12?
A) Definitely yes
B) Definitely no
C) Probably yes
D) Cannot be decided

Question

Quizplus · Accepted Answer

Given the demand function Q = 5 - 2P, where Q is the quantity of videos rented and P is the price per rental, we can calculate the total cost for renting videos both with and without the membership. Without the membership, the cost per rental affects the quantity rented directly. With the membership, the price per rental is $0.5, and there's an additional $12 annual fee. The demand function suggests that as the price decreases, the quantity of videos rented increases. However, the question is whether the savings from the lower rental cost ($0.5 per rental) plus the membership fee ($12) will be less than renting without the membership at varying prices. Since the demand function does not provide specific information on how many videos will be rented or the comparison of total costs with and without the membership, we cannot directly calculate the savings or overcost from purchasing the membership. However, given the structure of the demand function and the costs involved, we can infer that without knowing the original price per rental (P) before the membership discount, we cannot definitively say if the membership will save money. The choice "Definitely no" suggests a misunderstanding of the economic analysis required to make such a decision, as the decision heavily depends on the number of videos rented and the original price per rental. A more thorough analysis, considering these factors, would be required to make an informed decision.

If Your Demand for Renting Videos Is Q = 5